My initial reaction after reading
Piaget in graduate school could be summed up as something very similar
to :

"Who gives a frog's butt? This is the stupidest, most
boring useless stuff I have ever read!'

(I did change my mind somewhat after a while -
keep reading - although I still stand firm on the boring part. Piaget in
the original is a great cure for insomnia. Maybe it's better in French.)

Being the good student that I was, though, I assumed that
perhaps it was because I was just reading the textbooks' descriptions of
Piaget. After all, he must be important because most of the people in developmental
psychology, particularly in the cognitive development area, seemed to think
he was the best thing to come along since fry bread. So, ===== drum roll
here and be impressed, ==== I decided to go ahead and read Piaget's books
for myself. After plowing through many hundreds of pages of descriptions
of "ontological epistemology" (I am not making these words up) and more
hundreds of pages of discussions of how children's morality was revealed
through the rules they used in playing marbles (I am not making that up
either), I came to two conclusions:

1) As a student once said in a term paper, "Reading
Piaget is something like reading the instructions for putting my stereo
components together," and

2) Piaget does actually have some applications for educating
children, although, in my own personal opinion, he could have done a heck
of a lot better job at laying out those applications.

The impression I got, which I think is accurate, is that
Piaget was really interested in studying child development purely out of
scientific curiosity, and not that concerned with turning his theory and
findings into practical applications. It just happened to turn out that
there were some practical applications.

PRACTICAL APPLICATIONS OF PIAGET'S FINDINGS ON CHILDREN'S
COGNITIVE DEVELOPMENT

1. Decentering -- children in middle childhood become
capable of considering more than one aspect of an object or situation at
a time. Their thinking becomes more complex. For example, they can understand
that the area of a rectangle is determined by the length AND width.

2. Children's understanding is based on their concrete
experiences. So, if you are teaching children how to find area, you are
going to have a lot more success if you have them measure a lot of rectangles
than if you just give them a formula and expect them to apply it in general.
Your best bet is to have them measure rectangles on pieces of paper, have
them measure their desks, tiles on the classroom floor, etc. The same is
true if you are teaching about social studies.

A GREAT EXAMPLE OF CONCRETE LEARNING
IN SOCIAL STUDIES

How do you teach children about third-world countries,
inequities in income, etc.? One terrific example I witnessed was a unit
for third-graders on a South American country. The teacher explained that,
in this country, 90% of the people lived in poverty. They did not have
enough to eat; they did not have school supplies; they did not even have
desks in many of the schools. Then, she assigned 27 of her 30 students
to be poor. She took their chairs away and made them sit on the floor.
She gave them one box of broken crayons to share among them. She took their
snacks that they had brought from home and gave them instead one small
package of broken crackers to share. The three lucky "rich" children, on
the other hand, each had their own box of 64 brand new crayons, their own
lunches, and, of course, their own desks. Years later, the children who
were in that class still talk about what they learned about Chile.

Most teachers tend to follow Piaget's ideas on concrete
learning of children of this age, even if they are not as elaborate as
the example above. This is why, in elementary school social studies programs,
children learn about concrete aspects of other cultures, such as dress,
food, industries and the daily life of children in those societies, rather
than abstract notions such as the countries' political systems.

3. Conservation - that quantity, weight, etc. cannot be
judged just on appearances. While all of the discussion on conservation
of this and that may seem boring at first, and somewhat pointless, it really
isn't. What children are learning is to reason out things, some basic,
IMPORTANT fundamentals of mathematics for example:

A= A A + 0 = A
Identity. Something equals itself, and anything plus zero still equals
itself. If there were seven coins in a row before, and you didn't add any,
then there are still seven coins there. It doesn't matter if you spread
them out, stacked them up or put them closer together . Even if it LOOKS
as if there are more or less, there really is still the same number.

A- B + B = A Reversibility
- when you do something, whether it is squish a ball of clay flat or subtract
a number, you can do it in reverse and end up to where you were before,
with the same thing.

=====>>> AND ANOTHER THING--- METACOGNITION <<<=====

OR

WHY LITTLE KIDS SOMETIMES THINK MATH IS HARD

Metacognition was not one of Piaget's ideas but part of
cognitive learning theories which came later, particularly information
processing theory. I don't think that particular fact is as important as
the application of it. Metacognition is, literally, thinking about one's
own thinking. It is, as your textbook says, the ability to select the appropriate
strategies to use in the right situation.

I have an eleven-year-old and a twelve-year-old daughter.
Both are very intelligent. It is not just I who say so, but also the schools
which have one in an advanced program and offered to skip the other a grade.
Yet, they both have some trouble with math, especially word problems. Problems
like the one below cause them to be totally frustrated.

Jennifer met her friend at 7:30 pm. She had
$12 and she bought a hamburger at $2.25, french fries for $1.75 and a milk
shake. She had six dollars left over and spent it on video games. She went
from the arcade to her friend's house and got back home at 10:00. How much
did her milk shake cost?

It is not that they can't add or subtract, it is that they
don't know when to do which. They don't know what data is irrelevant. To
help children at this age, teachers (and parents) should be instructing
them to:

A) Identify relevant and irrelevant information.
What time she left, where she went and when she got home has nothing to
do with it. My youngest daughter calls all people in word problems "Bob",
even if they are female. If there are two or more people, she calls them
Bob1, Bob2, etc. It is her way of reminding herself that what the person's
name is has nothing to do with the right answer and it doesn't matter if
you can read or pronounce their name.

B) Identify the correct steps to take in solving a
problem. In this example, you started out with
$12, and after you ate, you had $6 left. So, first you figure out how much
your meal cost. Next, you figure out how much the french fries and hamburgers
together cost. Then you figure out what the difference is between the cost
of the hamburger + fries and your total meal. That is the cost of your
shake.

C) Identify which operations to perform. In this
case, first you subtract six from twelve, then you add $2.25 and $1.75
and then you subtract that amount from six. (And yes, I do know there are
other ways you could have solved this problem!)

Although the examples above focus mostly
on mathematics (for one reason, because that is what I used to teach),
the same processes of cognitive development apply to many different situations.
One that jumps to mind is doing the laundry. We live in an apartment building
in a two-story apartment. The laundry room is downstairs in an underground
garage, and you have to go outside to get to it. The door to get into the
garage and the laundry room are both locked. In case you are interested,
this is because, while Santa Monica is a fairly affluent area, we have
a very large population of homeless people, and many of the elderly people
in our building would get quite upset when they went downstairs to do laundry,
particularly after it had been cold or rainy the night before, and would
find someone sleeping next to the dryers. Actually, my husband used to
get upset, too, and he's not elderly.

ANYWAY, to get back to the subject, there are a number
of steps involved in doing the laundry. First, get your dirty clothes together,
then, take them downstairs, don't forget to take the keys to the laundry
room, don't forget to take quarters to put in the washer. Remember to bring
the keys back upstairs with you instead of locking them in the laundry
room. Go back downstairs and put the clothes in the dryer. Remember to
bring quarters to put in the dryer. Remember to bring the keys back upstairs
with you. Don't forget to go back and get your clothes out of the dryer
and bring them upstairs. Bring the keys with you. It is just because of
the incomplete development of metacognition in middle childhood that I
have four extra sets of keys. I cannot count the number of times a child
has come back upstairs because they have either forgotten money for the
machines, forgotten to bring keys, or locked the keys in the laundry room.
Sometimes they have locked the keys in the laundry room when they took
the clothes down to put them in the washer, forgotten about it, taken another
set of keys, and locked them in the laundry room after they put the clothes
in the dryer. This is why I have four extra sets of keys. I remind myself
that they are not doing this deliberately but that it is evidence of incomplete
development of metacognition. I remind myself of this frequently. That
way I do not kill them.